Problem: Rewrite as a simplified fraction. ${0.5\overline{1} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 51.1111...\\ 10x &= 5.1111...\end{aligned}}$ Subtracting the two equations, we have: ${90x = 46}$ ${x = \dfrac{46}{90}} $ ${x = \dfrac{23}{45}} $